Peter works as a delivery person for a bike shipping company. The graph shows a linear model for his delivery times on different days.

(a) what is the equation of the line, first written in point-slope form and then written in slope- intercept form? show how you determined the equation.

(b) based on the linear model, predict how long it initially took peter to deliver his packages (y-intercept) approximately how much did his delivery time decrease per day (slope)? Complete sentences

Answer/Step-by-step explanation:

a. Using a point on the graph, (6, 12), and the slope of the line, we can first generate an equation in the point-slope form, given as , where,

m = slope, and (a, b) is a point on the line.

Using two points, (6, 12) and (3, 21), let's find slope, m.

Using a point (6, 12) and slope, m = -3, generate an equation in the point-slope form by substituting a = 6, b = 12, and m = -3 in .

✅Equation in point-slope form would be:

Rewrite this to make it be in the slope-intercept form, .

Add 12 to both sides

✅The equation in slope-intercept form is

b. ✍️Based on the linear model, , the 30 represents b = y-intercept.

✅Therefore, it took Peter 30 mins long initially to deliver his package.

✍️Based on the linear model, , "-3" represents the slope.

✅Therefore,  Peter's delivery time decreased 3 mins per day.

x is the total time in minutes for the free response

you are given number of questions as 15 - m and time per item as 8 minutes

to find x multiply the two givens together:

x = 8 * (15-m) = 8(15-m)